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Astronomy Problems (Homework) 3 Solutions

Astronomy Problems (Homework) 3 Solutions - Homework 3...

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Homework 3 University Astronomy 4/23/10 1 University Astronomy 1017-301 Homework Assignment 3 Instructor: Dr Andrew Robinson Due Date: Friday, 16 April 2010. To tackle some of the following problems you will need to do some research, using either the textbook or other resources, to find various pieces astronomical data and the values of certain physical constants. For calculations, show all your workings in order to receive full credit . 1. In an analysis of the spectrum of a star, you measure the wavelength of the H β line of hydrogen to be λ =485.3. The rest (laboratory) wavelength is λ 0 =486.1 nm. a. What is the radial velocity of the star relative to Earth? b. Is it possible to determine the speed of the star? If not, what other information is necessary? c. What would be the measured wavelength of the H α line ( λ 0 = 656.3 nm) 2. The absolute visual magnitude of the Sun is M V = 4.82; its apparent visual magnitude is m V =–26.8. Alkaid, an A1V star, has an absolute magnitude M V = –0.59 and apparent magnitude m V =1.86. a. What is the luminosity of Alkaid, relative to that of the Sun? b. What is the distance to Alkaid, in parsecs? a) We use the Doppler formula (Lecture 9, slide 27): Δλ / λ 0 = v r /c with Δλ = 485.3-486.1 = -0.8 nm and λ 0 = 486.1 nm. Thus v r = c Δλ / λ 0 = -494 km/s. b) The Doppler shift only tells us the radial velocity – the component of the star’s velocity in our direction. In order to determine the speed , we also need to know the tangential component perpendicular to our line-of-sight, v t . In principle we could get v t from the star’s proper motion, but we don’t have this information, so we can’t determine the speed in this case. c) We have determined v r from the Doppler shift in the H β line. We can now use this to get the Doppler shift in H α : Δλ = λ 0 (v r /c), where λ 0 = 656.3 nm. Using v r = -494 km/s, we get Δλ = -1.08 nm, hence since Δλ = λ - λ 0 , =655.2 nm
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Homework 3 University Astronomy 4/23/10 2 3. Find the following stars using the StarGazer program. Click on the star to display the Info panel, and record the name, spectral type, distance in parsecs, absolute magnitude and surface temperature in a table. Using this information, estimate or calculate the following additional properties for each star: a. What (if any) absorption lines would you expect to find in the spectrum of the star (see Table 15-1 in the textbook, or the similar table in the lecture 10)?
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Astronomy Problems (Homework) 3 Solutions - Homework 3...

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